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arXiv · 0901.4616

Is the critical percolation probability local?

Itai Benjamini·Asaf Nachmias·Yuval Peres
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Abstract

We show that the critical probability for percolation on a d-regular non-amenable graph of large girth is close to the critical probability for percolation on an infinite d-regular tree. This is a special case of a conjecture due to O. Schramm on the locality of p_c. We also prove a finite analogue of the conjecture for expander graphs.

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Itai Benjamini, Asaf Nachmias, Yuval Peres. 2009-01-29. Is the critical percolation probability local?. https://arxiv.org/abs/0901.4616

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